A comparison of two quadratic approaches to hedging in incomplete markets

This paper provides comparative theoretical and numerical results on risks, values, and hedging strategies for local risk-minimization versus mean-var iance hedging in a class of stochastic volatility models. We explain the th eory for both hedging approaches in a general framework, specialize to a Ma rkovian situation, and analyze in detail variants of the well-known Heston (1993) and Stein and Stein (1991) stochastic volatility models. Numerical r esults are obtained mainly by PDE and simulation methods. In addition, we t ake special care to check that all of our examples do satisfy the condition s required by the general theory.